Structural Controllability of Temporally Switching Networks

In this paper, the controllability problem is addressed for temporally switching networks and the associated temporally switching systems. The state controllability criterion of temporally switching systems is firstly obtained, which stands for structural controllability of temporally switching networks with the same structure. With a new temporal interpretation of the dilation and intersection concepts, some algebraic and graphic criteria are precisely derived. Specifically, it reveals that the essence for the structural controllability is the existence of n temporally independent walks (the n-walk theory), which generalizes the classical concept of cactus in graph theory to temporal networks. Furthermore, from the perspective of the new n-walk theory, its uniqueness makes the notion of strong structural controllability more precise and clearer for temporal networks. This comprehension of the (strong) structural controllability concept not only is of particular advantage for more in-depth studies of network control problems, but also provides useful guidance for constructing controllable temporal networks.